Multiclass is probably good to ban because your more like to serious weaken a character than anything else. A monk/sorcerer is going to fall way behind the rest of the party.
I've always disagreed with this. Perhaps for pure combat, multiclassing weakens you, but none of my multiclassed characters ever felt weak to me. They felt fleshed out. People change, they grow, they become something else than they decided to when they were 18. Deals are made. Alliances forged. Weaknesses revealed that the character wants to improve upon. The Sorcerer who decides they are tired of always being weak and frail, so they start training to be a Fighter. The Bard who wants to play music better than anyone, then finds himself face to face with a Devil that can make it happen. The Barbarian who realizes he was called to be the servant of his god, thus becoming a Cleric. Or paladin. Or whatever.
These characters are fun. Doing it on a metagaming basis, sure they're a pain. You have to focus pretty hard on making it work from a numbers standpoint. "Do I want the extra attack, or should I just take the levels in Monk now?" My brother had that option. He was an Eldridge Knight, and after the first four levels, they had some downtime before they actually grew to level 5. He said his character went North, found a monastery and started training to control his inner magic (we had the Eldritdg Knight powers be Sorcerer based instead of Wizard). I told him about the Monk's Way of the Four Elements, and he said it was perfect, so now his Fighter 4 is a Monk 1, and is training to get those powers. That's how he interoperates "Control his inner magic". So he loves his character even more, even if he doesn't have the second attack that the party's Paladin and Battle Master have, and even the Party's Bladesinger will have at level 6. It's not power gaming. It's just gaming. Making whatever decision is important to the player. And he hasn't shown any indication that he feels left out as far as damage is concerned, because he loves his character.
I had a Rogue Warlock that I loved. He was a master at manipulating people. He was great out of combat. Basically the party face, using Silent Image to wreak all kinds of havoc. But he sucked at fighting. And I didn't really care. He was good enough, and used his intellect more than his fighting skills.
It can work. It does work. You don't have to 'keep up with the Joneses' to have a good time. Let them play their character, and during the course of the game, if it makes sense for them to multiclass, let them multiclass. If their Barbarian decides he is connected to nature, and wants to become his totem spirit in body, then let him multiclass a few levels in Druid as he becomes attune to nature. That's awesome.
Now, if they're just taking multiclasses to fulfill a build, and to metagame, that's different. As it was said before, if there's no reason to become a paladin, then don't allow that. It's not in the game. I would only allow mutliclassing (if starting at level 1) if it made sense in game. If starting at higher levels, you have to justify why your character has these different classes. But I never completely disallow it.